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lfunc_lfunctions • Show schema
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{'Lhash': '2453299654794944073367254830307', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.1376556341957407, -1.3060396846890552], 'a4': [0.0, 0.0], 'a5': [3.194996831770019, 0.0], 'a6': [0.0, 0.0], 'a7': [2.612890993389477, 0.4156929836599998], 'a8': [0.0, 0.0], 'a9': [-0.4114793159653739, -2.9716468115394647], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.024460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.1376556341957407, 1.3060396846890552]]], [7, [[1.0, 0], [-2.612890993389477, -0.4156929836599998]]]], 'bad_primes': [2, 3, 7], 'central_character': '504.457', 'coefficient_field': 'CDF', 'conductor': 504, 'conductor_radical': 42, 'conjugate': '2137810162910774863011585556131', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.1376556341957407, 1.3060396846890552]], [[1.0, 0], [-3.194996831770019, 0], [5.0, 0]], [[1.0, 0], [-2.612890993389477, 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'9.452768168134696222200794945770093', '9.936112661126913545098242858206864', '10.82058796847319383090111753426845'], 'prelabel': '2-504-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.20847192905755055, 'root_number': '0.7930882034857698 + 0.6091068063088068*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.104235964529', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93531218645993535706308008441', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.81654674367955284402719369777', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.54967196299154174876290678551', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.024460261872533, 'bad_primes': [2, 3, 7], 'central_character': '63.16', 'conductor': 504, 'conductor_radical': 42, 'degree': 2, 'index': 19, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/504/2/t/c/457/9'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-504-63.16-c1-0-19', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-504-63.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0061057454363, 'root_angle': 0.10423596452877527, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93531218645993535706308008441', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2453299654794944073367254830307', 'Lhash_array': ['2453299654794944073367254830307'], 'label': '2-504-63.16-c1-0-19', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/504/2/t/c/457/9'}